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Question Number 175923 by CrispyXYZ last updated on 09/Sep/22

what are the differences among “ if ”, “ only  if ” and “ if  and  only  if ”?

$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{differences}\:\mathrm{among}\:``\:{if}\:'',\:``\:{only}\:\:{if}\:''\:\mathrm{and}\:``\:{if}\:\:{and}\:\:{only}\:\:{if}\:''? \\ $$

Answered by Vynho last updated on 09/Sep/22

if=necessary condition  only if = sufficient condition  if and only if=necessary and sufficient condition

$${if}={necessary}\:{condition} \\ $$$${only}\:{if}\:=\:{sufficient}\:{condition} \\ $$$${if}\:{and}\:{only}\:{if}={necessary}\:{and}\:{sufficient}\:{condition} \\ $$

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